2.2 System Model
2.2.2 Asynchronous TWRN model
The asynchronous TWRN is studied in Chapter 4, where we assume perfect carrier frequency synchronisation and focus on the carrier phase and timing
syn-2.2. System Model
chronisation in the AF-TWRNs. The asynchronous TWRN model is illustrated in Fig. 2.5. Due to the lack of synchronisation, signals transmitted by source nodes do not perfectly align. One signal starts first with a few symbols that do not interfere with the other signal, while the second signal ends last with a few symbols that do not interfere with the first signal. As shown in Fig. 2.5, there are overlapped and non-overlapped symbols in the received signal at relay. The carrier phase synchronisation is performed based on the whole signal in Chapter 4. In addition, the symbols of each signal do not perfectly align in the asyn-chronous TWRNs. As a result, there exists a symbol offset and the estimation of this symbol offset is known as symbol synchronisation. In the special case, where the symbols of each signal align, there only exists a frame offset between signals.
This case is referred to as the frame asynchronous TWRNs, as shown in Fig. 2.6.
The estimation of the frame offset is known as frame synchronisation.
The following assumptions have been made throughout Chapter 4 of the the-sis:
1. Amplify-and-Forward relaying scheme at relay node.
2. MPSK: In the asynchronous AF-TWRN, we employ MPSK modulation and demodulation schemes.
3. Channel Model: Quasi-static and frequency flat-fading channels are con-sidered and the channel is assumed to be fixed and flat over one frame.
For frequency-selective fading channel, orthogonal-frequency-division mul-tiplexing (OFDM) technique effectively converts a single frequency-selective fading channel into multiple parallel quasi-static flat fading sub-channels.
The proposed synchronisation and channel estimation algorithms can be applied to estimate channel parameters and the time offset of different fre-quency sub-bands one by one;
2.2. System Model
T
1R T
2Time Slot 1 Time Slot 2
Figure 2.5: Asynchronous two-way relay network.
T
1R T
2Time Slot 1 Time Slot 2
Figure 2.6: Frame asynchronous two-way relay network.
4. Over one frame, the timing offsets are modelled as deterministic but un-known parameters. Perfect carrier frequency synchronised is assumed. Typ-ically, carrier frequency can be recovered from the received noisy signal by means of a suppressed carrier phase-locked loop (PLL) [84].
2.2.3 Contention-Based Multiple Access Network
The contention-based multiple access network considered in Chapter 5 has N nodes, contending to communicate with the access point over a single communi-cation channel, as shown in Fig. 2.7. We study the local medium access process of a node under the carrier sense multiple access (CSMA) random access mecha-nism, given the local packet arrival rate λ and the total number of nodes N .
The following assumptions have been made throughout Chapter 5 of the the-sis:
1. There is no communication between N nodes, which only transmit to the access point under contention-based media access scheme CSMA. Under CSMA access scheme, each user performs carrier sensing before sending a
2.2. System Model
packet, in order to sense the actions of other users. If the channel is sensed idle (i.e., no user is transmitting), the packet is transmitted. If the channel is busy (i.e., some other user is transmitting), the backoff mechanism is employed to delay the packet transmission for a random amount of time to avoid collisions.
2. The backoff algorithm is employed to resolve contention among transmitting nodes. If the node senses a busy channel or has a transmission failure, it waits a random amount of time before the next channel access in order to avoid repeated collisions. However, the binary exponential backoff (BEB) algorithm is not considered and we employ the proposed backoff algorithm for contention resolution.
3. The total number of the nodes in the network is assumed known to all the nodes and all the nodes share the same average packet arrival rate λ.
R T 1
T 2 T i
T N
Figure 2.7: Multiple Access Model with N nodes transmitting to one Access Point.
Chapter 3
Semi-Blind Low Complexity
Channel Estimation Algorithms in AF-TWRNs
In order to improve the spectral efficiency in the physical (PHY) layer of the open systems interconnect (OSI) model, the relay schemes are considered in this chap-ter. Under the assumption that the carrier frequency, carrier phase and timing are synchronised among all the nodes, we investigate the channel estimation issues in the amplify-and-forward two-way relay networks (AF-TWRNs). To our best knowledge, a deterministic maximum likelihood (DML) channel estimator and a modified constrained maximum likelihood (MCML) estimator are proposed in [60] for semi-blind channel estimation in the synchronous AF-TWRNs. However, the DML and MCML algorithms have to rely on numerical solutions by using optimisation tools, due to the non-convex optimisation functions for channel es-timation. In order to make the existing semi-blind channel estimators practical, we propose a low complexity semi-blind channel estimation algorithm, referred to as the low complexity maximum likelihood (LCML) estimator, to estimate general non-reciprocal flat-fading channels by using only one training symbol per
3.1. System Model
estimation in AF-TWRNs. We formulate a convex maximum likelihood estima-tion funcestima-tion and derive a closed-form channel estimator. Then we propose the modified low complexity maximum likelihood (MLCML) channel estimator, by employing the BPSK modulation structures, to improve the MSE performance of the LCML channel estimator in the case of BPSK. The MLCML channel es-timator not only achieves a closed-form channel estimation, but also improves the MSE performance of the LCML estimator for BPSK. We analyse the pro-posed LCML and MLCML algorithms theoretically and prove that the LCML channel estimator is consistent and unbiased. The MSE performance evaluation shows the derived channel estimators approach the true channel in either high signal-to-noise ratio (SNR) or large frame length scenario.
3.1 System Model
A typical half-duplex TWRN over quasi-static flat-fading [90] channels is consid-ered in this chapter. The system is composed of three nodes, two source nodes T1 and T2 and one relay node R. Each node is equipped with a single antenna.
Two source nodes are out of each other’s transmission range. We assume perfect frequency and timing synchronisation [84] among these nodes. In the scenario of a frequency selective channel, the proposed channel estimation algorithms can be applied to estimate channel parameters of different frequency sub-bands one by one.
Each signal transmission process occupies two time slots. In the first time slot, two source nodes T1 and T2 simultaneously transmit signals to the relay node R. As MPSK modulation and demodulation are employed, the transmitted base band signals are s1 = √
P1ejϕ1 and s2 = √
P2ejϕ2, respectively. P1 and P2 are transmit powers of T1 and T2, respectively. In TWRNs, the most common
con-3.1. System Model
vention is to set P1 = P2. ϕ1 and ϕ2 are MPSK modulated phases, which are independent and uniformly distributed in the set SM = {2π(lM−1), l = 1, ..., M} where M is the modulation order and j =∆ √
−1.
In the first time slot, the received signal at the relay node is given by
r1 = h1s1+ g1s2+ n1. (3.1) In (3.1), n1 is additive white Gaussian noise (AWGN) distributed in CN (0, σn2), which represents the complex normal distribution with zero mean and variance σn2. h1and g1are complex coefficients of flat-fading channels T1 → R and T2 → R, respectively. Since non-reciprocal channels are considered in this paper, the com-plex channel coefficients of R → T1 and R → T2 are denoted as h2 and g2, respectively. Channel coefficients h1, h2, g1 and g2 are modelled as independent and identically distributed (i.i.d) in CN (0, σc2) and remain fixed during one esti-mation process.
In the second time slot, the relay node purely amplifies the received signal r1
and then broadcasts the amplified signal Ar = Kr1, where K is the power scaling factor. To maintain an average power of Pr at the relay node over a long term, the expression K =√σ2 Pr
cP1+σc2P2+σn2 is used in this chapter, where Pr denotes the transmit power of R. Here, we assume P1, P2, σc2 and σ2n are prior known to R. Without loss of generality, channel estimation and signal detection at T1 are studied. The received signal at T1 is obtained as
r = Kh1h2s1+ Kg1h2s2+ Kh2n1+ n2, (3.2) where n2 is AWGN distributed in CN (0, σn2).